To answer your newer question,
If there isn't a way to see a log of when someone logged out, is there
at least a way to tell who is currently logged in?
You can only record when someone takes an action to log out, i.e. presses the logout button, you cannot record someone whose session has expired and therefore required to go through the login process again....
With Admintools it keeps a history of banned IP's as well as the currently banned IP's. If you check the #__admintools_ipbanhistory table via phpMyadmin or whatever you use you will probably see the people or their IP's listed. I have found clearing this table of the entries has solved a similar issue that I have had in the past.